General Relativity field equations [1]:
Gµν = G*Tµν...... (EQ.1).
It is a relation between the matter field (energy-momentum field) Tµν and the spacetime field Gµν, where the gravitational constant G is the conversion factor between the dimensions [2].Einstein constructed this relation without explaining why the spacetime field and the matter field are in such a way, but rather assumed that nine times out of ten, they would be in such a way. He also did not explain why the spacetime field Gµν is described by curvature and not by some other parameter. Obviously, we must find the exact physical relationship between them, i.e., why Tµν must correspond to Gµν, in order to ensure that the field equations are ultimately correct.
We know that matter cannot be a point particle, it must have a scale, and matter cannot be a solid particle, it must be some kind of field. The fact that matter has a scale means that it has to occupy space-time; the fact that matter is a field means that it is mixed with space-time, i.e., matter contains space-time. So, when applying Einstein's field equations, how is matter's own spacetime defined? Does it change its own spacetime? If its own energy-momentum and structure have already determined its own spacetime, should the way it determines its own spacetime be the same as the way it determines the external spacetime? If it is the same, does it mean that the spacetime field is actually a concomitant of the matter field?
If one were to consider a gravitational wave, one could think of it as a fluctuating spacetime field that propagates independently of the material source after it has been disconnected from it. They have decoupled from each other and no longer continue to conform to the field equations (EQ.1). Although gravitational waves are the product of a source, the loss of that source prevents us from finding another specific source for it to match it through the equation (EQ.1). Just as after an electron accelerates, the relationship between the radiated electromagnetic wave and the electron is no longer maintained. Does this indicate the independence of spacetime field energies?
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Related questions
♛ “Does the Energy Tensor Tµν in the Field Equations Contain the Energy-momentum of the Spacetime Field?”：https://www.researchgate.net/post/NO37Doubts_about_General_Relativity_2-Does_the_Energy_Tensor_Tmn_in_the_Field_Equations_Contain_the_Energy-momentum_of_the_Spacetime_Field
♛ “Is the Geometry Interpretation of Gravity a Paradox?”：https://www.researchgate.net/post/NO36_Doubts_about_General_Relativity_1-Is_the_Geometry_Interpretation_of_Gravity_a_Paradox
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References
[1] Grøn, Ø., & Hervik, S. (2007). Einstein's Field Equations. In Einstein's General Theory of Relativity: With Modern Applications in Cosmology (pp. 179-194). Springer New York. https://doi.org/10.1007/978-0-387-69200-5_8
[2] “The Relationship Between the Theory of Everything and the Constants of Nature”：https://www.researchgate.net/publication/377566579_The_Relationship_Between_the_Theory_of_Everything_and_the_Constants_of_Nature_English_Version
The spacetime metric, determined by matter, is the solution of Einstein's equations. That's all, nothing more and nothing less.
"It is a bad habit of physicists to take their most successful abstractions to be real properties of our world." (N. David Mermin)
If we consider space-time as an abstraction of the trajectories of material objects, there is no difference between "curvature of space-time" and "curvature of matter".
The scientific answer to question “what is Gravity” is given in a few SS posts on page 1 in https://www.researchgate.net/post/NO36_Doubts_about_General_Relativity_1-Is_the_Geometry_Interpretation_of_Gravity_a_Paradox/1,
first of all that Gravity fundamentally is only some fundamental Nature force, which, as all other – Weak, Electric, Strong/Nuclear, Forces, exists and acts in the Matter’s fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct),
- by that particles [so further bodies, etc.], again as that happens at actions of all other Forces, radiate Gravity Force real mediators, intensive flows of which compose “gravitational fields” in 3D space, again, as that all other Forces do;
- and at that, again as that happens at actions of all other Forces, at Gravity action fundamentally nothing happens with the space/time/spacetime above. More see the link above and the linked papers in this link, where the Shevchenko-Tokarevsky’s Planck scale informational physical model, including initial Planck scale Gravity model is presented.
So only a note to
“…【NO.39】… - Who should determine the spacetime metrics of matter itself?…..”
Really metrics of the spacetime above indeed “is determined by matter”, as that follows from the rigorous scientific definitions of the absolutely fundamental phenomena/notions “Space”, and “Time”, which can be, and are, given only in framework of the SS&VT philosophical 2007 “The Information as Absolute” conception, the link again see the link above:
- the spacetime has fundamentally unique one time dimension,ct,
- while the number [4+4] and nomenclature of the space dimensions are determined by number and nomenclature of degreases of freedom at changing of states of the Matter’s ultimate base –primary elementary logical structures – (at least) [4+4]4D binary reversible fundamental logical elements [FLE], which compose the (at least) [4+4]4D dense FLE lattice that is placed in the space.
- while everything in Matter/matter is/are only some disturbances in the lattice.
So indeed, metrics of the space is determined by “metric of matter”, though more rigorously scientifically – yet by “FLE metric”, the fundamentally infinite Matter’s spacetime “immediately appeared” in parallel just when first FLE was created,
- while “FLE/matter metric” is determined by the conditions above – FLE must be binary [for this is necessary 3 degreases of freedom and 3XYZ dimensions], reversible [for this is necessary 1 degrease of freedom and one cτ-dimension], and at least 4 logical marks/degreases of freedom [and g,w,e,sdimensions] that determine the at least 4 Forces above action. That’s all.
Though, of course, here the question appears – Who did this “FLE metric” designed/determined? With a well non-zero probability that was done by some Matter’s Creator, etc., but this point is now rather far from physics.
More see the SS first of all April 19, posts, in the linked above thread..
Cheers
Dear Walter Smilga
Thanks for your answer!
"It is a bad habit of physicists to take their most successful abstractions to be real properties of our world." (N. David Mermin).
Couldn't agree more with that sentiment. But I don't quite understand your sentence：“If we consider space-time as an abstraction of the trajectories of material objects, there is no difference between "curvature of space-time" and "curvature of matter". ”
What does“the trajectories of material objects”means？object self? a good idea.
Best Regards, Chian Fan
Dear Stam Nicolis
Thank you for your answer! You said "The spacetime metric, determined by matter, is the solution of Einstein's equations. That's all, nothing more and nothing less."
You mean Einstein's Equations determines all spacetime metrics, Including the space-time of matter itself? Then, in essence, it is the same as saying that all spacetime metrics are part of matter, similar to Walter Smilga 's point above, that a spacetime metric is a "curvature of matter".
For example, who determines the spacetime of an electron? If the electron is a field, even though we can define a radius for it that describes the size, it has no truncated boundaries when viewed as a whole. So does it have the same mechanism of action for its internal and external spacetime metrics? Does the electron field represent all mass/energy and determine all spacetime metrics? Is this the relationship between fields and spacetime?
We know that gravitational fields affect the frequency of photons, so does a photon traveling in free space affect the spacetime around it?
Is it the starting point of quantum gravity theory to consider the effect of photons and electrons on the spacetime metric in this way?
Please, if it's convenient, I look forward to your answering the following two questions together.
https://www.researchgate.net/post/NO38Doubts_about_General_Relativity_3-Are_Space-Time_Curvature_and_Expansion_Two_Different_Geometrical_Mechanical_Properties
https://www.researchgate.net/post/NO37Doubts_about_General_Relativity_2-Does_the_Energy_Tensor_Tmn_in_the_Field_Equations_Contain_the_Energy-momentum_of_the_Spacetime_Field
Best Regards, Chian Fan
The spacetime metric-in the presence of matter-is determined by Einstein's equations, by virtue of the fact that the energy-momentum tensor of matter appears on the RHS of Einstein's equations.
In the absence of matter, Einstein's equations have as solution the flat metric, describing Minkowski spacetime, if the cosmological constant is zero; if it isn't zero, the solution is de Sitter spacetime, if the cosmological constant is positive or anti-de Sitter spacetime, if the cosmological constant is negative.
In the presence of matter, Einstein's equations acquire a non-zero RHS, essentially equal to the product of Newton's constant and the energy-momentum tensor of matter.
The equations of motion for matter, also, depend on the metric; the equations are coupled and are solved together.
However, since Newton's constant is dimensionful, it does matter that the--dimensionless--combination of Newton's constant and the ``typical'' energy of matter is a very small number, unless we're dealing with objects like the Earth (or more massive). That's why ordinary matter affects spacetime to a negligible extent and therefore spacetime can be taken to be flat for non-astronomical situations (the cosmological constant, too, doesn't affect this; that's why its name is appropriate, it is relevant for cosmological siuations), so an electron doesn't contribute to curving spacetime in any meaningful way; its equations of motion can be solved by taking the metric to be the flat metric, which is also a solution of Einstein's equations when the contribution of matter and of the cosmological constant can be neglected-and the appropriate boundary conditions, of course, have been imposed.
There's no particular ``origin'' in any spacetime, due to general coordinate invariance.
``Central objects'' make sense in the Newtonian approximation, not in spacetime.
de Sitter spacetime has a (past) singularity-in spacetime-not an origin. That singularity isn't ``anywhere in particular'', though.
``Origin'' refers to a coordinate system, a spacetime doesn't have a unique coordinate system.
The difference between an origin and a singularity is that the singular behavior of coordinate systems at an origin can be resolved by changing coordinate systems; the existence of spacetime singularities doesn't depend on the coordinate system chosen and is a property of the spacetime, whatever the choice of coordinate system.
Dear Chian Fan,
What I mean is simply this: The kinematics of a material body can be described by its position in time or by its trajectory in space-time. This trajectory will generally be curved by the forces acting on the body. Einstein took this curvature as the curvature of spacetime (cf. his paper of 1916). Einstein's spacetime can therefore be seen as an abstraction of all possible trajectories of a material object in a given environment.
The "bad habit" to take "abstractions to be real properties of our world" (Mermin) obscures this connection and opens the door to all kinds of misinterpretations.
Best regards,
Walter Smilga
Chian Fan,
"It isn't about doubts but about lack of knowledge."
The answer to your question is in this short YouTube video with Distinguished Theoretical Physicist and String Theorist Robbert Dijkgraaf.
https://youtu.be/-TGvde_mVXY?si=D7iP0xdjoKJrZyaJ
No metric has any particular origin and that includes the Kottler metric or any solution of Einstein's equations.
It would be useful to understand the difference between objects moving in space and time separately and spacetime.
The thread question is scientifically answered in SS post on page 1, and more in detail in links in the post; if quite briefly
- Gravity is fundamentally nothing else than some fundamental Nature force, and, as all other fundamental Nature forces, exists and acts in Matter’s fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct),
- and at existence and acting of Gravity Force, again as that happens for all other Forces, fundamentally cannot be, and so isn’t, any interactions between any/everything in Matter, including “masses”, with the spacetime. Including, of course, to spacetime no any “stresses” “energies”, etc. fundamentally cannot be transmitted, etc.
So considering of any other spacetime metrics besides the Cartesian one above really is fundamentally senseless.
[Note also that in mainstream physics only a part of utmost universal “kinematical” spacetime with metrics (cτ,X,Y,Z,ct), i.e. really space with metrics (icτ,X,Y,Z ), “i” is imaginary unit, i.e. Minkowski and pseudo Riemannian spaces is really of course erroneously postulated as the spacetime, where the space cτ-dimension with imaginary unit is postulated as the time dimension]
More see the SS pointed post and links in the post.
Cheers
Dear Issam Mohanna
Are you telling me that my question was already scientifically settled and my questioning it is my ignorance? No matter, we are all ignorant.
The link you provided is forbidden in my area, please summarize the content of the short video for us.
Best Regards, Chian Fan
Usually we think of gravity's relative manifestation in the microscopic space as being too small to have any substantial effect. But such an understanding is not without problems.
1) Generally we use the gravitational and electromagnetic force ratio of protons or electrons to assess their magnitude difference, which is roughly 10-36 when r is the macroscopic distance. This is indeed too big a difference. However, we must note that a small gravitational force is not the same as a zero gravitational force. There is a fundamental difference here. If we don't use ratio analysis, but instead consider the gravitational force alone, it is clear that the gravitational force Fg=Gme2/r2 increases dramatically as r decreases. If the electromagnetic force does not similarly increase at this point, or even the charge fails, then gravity undoubtedly becomes the dominant force at the microscopic level.
2) Do the Einstein field equations not apply to microscopic particles? Then we would have to make a change in Einstein's starting point for establishing the field equations, because the field equations are established without any energy level constraints. If the quantum level does not hold, then why does the macroscopic hold? Has mass changed qualitatively in any way from microscopic to macroscopic?
3) As long as we acknowledge the basis of Einstein's ideas in constructing the field equations, that mass generates a spacetime metric, how would it be more reasonable to proceed in the hope that Einstein's field equations would be quantized at both ends and linear at both ends?
Chian Fan,
If you are a nerd,you should be able (by) yourself to find a workaround to overcome the glitch that prevents you from having access to that YouTube video.
From the point of view of GR spacetime buoyancy, the real structure of spacetime develops event by event, and when the particle has passed the event shell, the curvature is updated and the correlation settles over the distance, and the existence of energy density in itself is not a prerequisite for the shape of spacetime. In accordance with the holographic principle, the event shell stores the curvature information in tidal stresses, which are bundled into shape by a continuous light-like waving as a manifold that preserves the momentums of the field parts. Other entangled quantum states can also be conserved as non-local hidden variables over the spacetime structure.
Spacetime geometry and matter content do not need to be separate - they can be modeled as a whole as 4-buoyancy with 4-density, which is mainly based on the motion state in the tangent plane of the local event shell, giving the equilibrium state of geodesics and density equally.
Gµν = G*Tµν...... Can be rewrite as g(mu,nu) = G(mu,nu,a,b)*T(a,b).
For simplicity we use G(mn,nu,a,b) as set of constants. Equations are nonlinear. Lets think if it's possible to split matter and and field like:
1: g(mu,nu)=0
2: T(a,b)=0
Further depends on our understanding of matter and field.
a. Does g depends on on matter (T)
b. Does T depends on field (g)
So in easy case its possible to have solutions for field without matter or for matter without field. And it's hard to see physical sense for such solutions.
The thread question is rigorously scientifically answered in SS posts o pages 1, 2. If quite briefly – Gravity fundamentally is nothing else than some fundamental Nature force, and as all other Forces, acts in the Matter’s fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct).
The spacetime, as that rigorously proven in the Shevchenko-Tokarevsky’s really philosophical 2007 “The Information as Absolute” conception, recent version of the basic paper see
https://www.researchgate.net/publication/363645560_The_Information_as_Absolute_-_2022_ed
- and more concretely in the Shevchenko-Tokarevsky’s Planck scale informational physical model, which is based on the conception, 3 main papers are
https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics
https://www.researchgate.net/publication/367397025_The_Informational_Physical_Model_and_Fundamental_Problems_in_Physics
https://www.researchgate.net/publication/369357747_The_informational_model_-Nuclear_Force
- fundamentally cannot be “contacted”, “dilated”, “curved”, etc., by anything in Matter, and so fundamentally cannot have other metrics than the above one.
What concretely really Gravity Force is see the Shevchenko-Tokarevsky’s 2007 Planck scale informational physical Gravity [and Electric Force] model either in section 6. “Mediation of the fundamental forces in complex systems” in 2-nd whole model paper link above, or in https://www.researchgate.net/publication/365437307_The_informational_model_-_Gravity_and_Electric_Forces
In 3-rd link of whole model the 2023 initial Planck scale model of Nuclear Force is presented; where it is rigorously scientifically shown that on Planck scale at least these 3 Forces above act by the same one scheme.
So, say, to that
“…Lets think if it's possible to split matter and and field like: …So in easy case its possible to have solutions for field without matter or for matter without field. And it's hard to see physical sense for such solutions.…..”
- [besides that in the GR there is no Gravity “field”, gravitational interactions are determined by “curved spacetime metrics”, which for/by some completely mystic reasons/ways has some “stress-energy”], note that really Gravity field – as fundamentally all other Forces fields without Forces charges – cannot exist without Gravity charge “gravitational mass”, and in Matter everything that has inertial mass, i.e. practically everything at all [besides the fields at least at statics] has gravitational mass.
More see the SS posts above and links in the posts.
Cheers
Dear Chian Fan,
You write
“…A good answer to each of the questions does not require many copies…”
- that looks as a bit questionable claim. There is nothing bad when good answers to scientific questions are repeated as some copies, besides in RG discussions that is simply convenient for readers, first of all for new in a thread ones.
While that
“… Please leave the opportunity for others to express different points of view and to see different points of view...”
- looks, since is addressed to SS posts, as a too questionable claim. Really in RG threads rather numerous posts contain quite “non-good” answers, and the posters are rather vivid, what essentially interfere with the readers, who really want to know good, i.e. really scientific, answers, to read them; in some cases that looks as some deliberate spamming.
At that I don’t write as a rule more one post/day; and, if the thread’s question is already answered, no more one notification to the readers above about where the answers are, than one post in a page. What evidently don’t disturb opportunity for others to express different points of view and to see different points of view. When, again, rather often it would be better if some strange scientifically points would not appear in threads at all.
Cheers
Its Bootstrap. System acts collectively , emerging , feedback loop of previous two state. No one is deciding or intervening the process. We as a scientist , having code, research finding must be repeatable , recreateble and universal. So while going through all these hundreds of steps ,we need a database and database manager. Maths served as Database Framework, Equation becomes an identifier, solutions as observable value.
Nature doesnt act as by Equations. We observe and try to fit it in a expression whatever is possible. Mathematical equations gave us solutions and approximations ,coincidently almost exactly similar to actions in Nature.
The fundamental constant 'h', 'c' and Higgs mechanism is responsible for all values of observable ,eigen values , solutions everything, the fine structure constant, coupling strength of field, instable heavy element decaying.
Did 'h' and 'c' and Higgs mechanism were predetermined by Nature ? Nope. Quantum fluctuations create a change ,either increase or decrease in Potential value of other particle/quanta. The Quantum Fluctuation is RANDOM. But isnt Quantum Fluctuation result of present values of Field , Particle , constant ? Yes. That indicate Quantum Fluctuation is pseudo Random.
Fluctuation behave by given Fundamental Values. Fundamental Values determine Fluctuation.
I think we have hit at a Feedback Loop, which never can be answered except in Higher Dimensions similar to our 3 + 1 Dimension.
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